Interpreting Tables and Graphs - SHSAT Math

1. The table shows the distribution of scores on a 10-point quiz taken by a class of 25 students. Based on the table, what is the median score?
   Answer: 7 With 25 students, the median is the 13th value when ordered. Cumulative counts: score 4: 2, score 5: 2+3=5, score 6: 5+4=9, score 7: 9+6=15, score 8: 15+5=20, score 9: 20+3=23, score 10: 23+2=25. The 13th student falls in the score-of-7 group. Distractor A (6) occurs if a student lands one group early. Distractor C (7.5) confuses 25 with 26. Distractor D (8) uses the mode of the upper half.
2. The histogram below displays the number of text messages sent by 40 teens in a day. Based on the graph above, what percent of the teens sent fewer than 60 text messages?
   Answer: 45% Bins below 60: [0,20): 6, [20,40): 5, [40,60): 7. Total = 18. 18/40 = 45%. Distractor A uses only the first two bins (11/40 ≈ 27.5%, rounded to 30%). C incorrectly includes [60,80). D sums bars above 60 instead.
3. Refer to the pie chart below. If the chart represents 360 total students, approximately how many selected "Drama" as their favorite elective?
   Answer: 60 The Drama slice is approximately 1/6 of the circle, and 1/6 of 360 is 60. Among the other choices, 30 would be 1/12 of the circle and a much slimmar slice of the pie. 90 would be 1/4 of the circle (about the size of "Art"). And 120 would be 1/3 of the circle.
4. The circle graph below shows how the 400 students at Lincoln Middle School commute to school. Based on the graph above, how many more students walk or bike to school than take the bus?
   Answer: 40 Walk = 25% of 400 = 100. Bike = 15% of 400 = 60. Bus = 30% of 400 = 120. Walk + Bike = 160. Difference: 160 - 120 = 40. Distractor A (20) comes from confusing percent with count. Distractor C (60) comes from using bike alone vs bus. Distractor D (80) is 2× the correct difference.
5. Use the table to answer the question. What is the median finishing time, in minutes, for the five runners listed?
   Answer: 118 Ordered times: 112, 116, 118, 120, 123. The middle value is 118; hence C is correct. Choices A and B pick lower‐ranked times; D selects one of the upper times, not the median.
6. Refer to the double-line graph below. On which day were the high and low tides at the same recorded height?
   Answer: Day 4 Both lines intersect at Day 4 at 2.1 m, so Day 4 is correct. Other days show different heights; thus choices A and C are wrong. They do match, so D is incorrect.
7. The box-and-whisker plot below compares test scores for Class X and Class Y. Based on the plot shown, which statement must be true?
   Answer: At least 75% of Class Y scored higher than at least 50% of Class X. Class Y's Q1 = 75 equals Class X's median, so Y's upper 75% all scored ≥ Class X's median, meaning they scored at or above at least 50% of Class X. A cannot be inferred (box plots show medians, not means). C is false: X range = 95-55 = 40, Y range = 100-70 = 30. D cannot be determined without class sizes.
8. Refer to the scatter plot below. Which statement best describes the relationship between study hours and quiz score?
   Answer: There is a strong positive correlation. Points trend upward from lower‐left to upper‐right, indicating more hours correspond to higher scores—a strong positive correlation. B reverses direction, C ignores clear trend, D is not visible in data.
9. The stem-and-leaf plot below shows the weights (in pounds) of 20 dogs at a veterinary clinic. Based on the plot shown, what is the positive difference between the mean and the median weight?
   Answer: 0.6 lb Read the 20 weights from the plot: 12, 15, 18, 21, 23, 25, 27, 29, 30, 32, 34, 34, 36, 38, 41, 44, 47, 52, 56, 58. Mean: the weights add to 672, so the mean is 672 ÷ 20 = 33.6 lb. Median: with 20 values, average the 10th and 11th values: (32 + 34) ÷ 2 = 33 lb. The positive difference is 33.6 − 33 = 0.6 lb. 1.0 lb comes from rounding the mean up to 34 before subtracting. Using only the 10th value, 32, as the median gives 1.6, which is close to 1.5 lb but still wrong; with an even number of values the median is the average of the two middle values. 2.0 lb comes from misreading the plot, such as dropping a leaf, which changes both the sum and the middle values.
10. The table shows the revenue (in thousands of dollars) for two stores over four quarters. Based on the table shown, in which quarter was Store B's revenue the largest percent of Store A's revenue?
    Answer: Q3 Ratios B/A: Q1: 36/60 = 60%. Q2: 45/75 = 60%. Q3: 56/80 = 70%. Q4: 54/90 = 60%. Q3 is largest. A student comparing raw differences (A-B) might mistakenly pick Q1 or Q2 where both are 24–30, or Q4 where B is highest in absolute terms.
11. The double bar graph below shows the number of hours five students spent studying and sleeping on a particular school day. Based on the graph shown, for how many of the students was the ratio of sleeping hours to studying hours greater than 3:1?
    Answer: 2 Ratios (sleep:study): Anna 9:2 = 4.5, Ben 8:3 ≈ 2.67, Carla 10:3 ≈ 3.33, Dan 7:3 ≈ 2.33, Eva 9:4 = 2.25. Only Anna and Carla exceed 3:1, so 2 students. A student who miscounts Carla (3.33 > 3) or mistakenly counts Ben (2.67) may pick 1 or 3.
12. Use the table to answer the question. Which grade has the highest percentage of students who responded "Yes" to the survey?
    Answer: 8th grade Percent Yes: 6th: 60⁄100 = 60%; 7th: 58⁄95 ≈ 61%; 8th: 70⁄110 ≈ 64%. Highest is 8th grade. Distractors pick smaller percentages or claim tie.
13. The double line graph below shows the monthly sales (in units) of two products, P and Q, from January to June. Based on the graph shown, during how many months was the combined sales of P and Q greater than 500 units AND the sales of Q greater than the sales of P?
    Answer: 2 Monthly values (P, Q, sum, Q>P?): Jan (200, 180, 380, no); Feb (220, 240, 460, yes); Mar (250, 280, 530, yes); Apr (300, 260, 560, no); May (280, 320, 600, yes); Jun (260, 240, 500, no). Both conditions met in Mar and May = 2 months. Feb fails sum>500. A student ignoring the '500' constraint picks 3; one overlooking Q>P in June picks 3 or 4.
14. Based on the pie chart below, which category receives exactly one quarter of the total budget?
    Answer: Maintenance The chart labels Maintenance at 25%, representing one quarter. Utilities (15%), Salaries (45%), and Technology (15%) are not equal to 25%, so those choices are wrong.
15. Use the frequency table to answer the question. What is the cumulative frequency for scores less than 70?
    Answer: 14 Adding frequencies: 50–59:5 and 60–69:9 gives 14. Other choices correspond to individual bin (A=9) or sums that include higher bins (C=17 adds 70-79, D=20 adds even more).
16. Based on the line graph below, during which two consecutive days did the plant grow the least?
    Answer: Day 4 to Day 5 Heights: Day1 = 12 cm, Day2 = 14 cm (+2), Day3 = 17 cm (+3), Day4 = 19 cm (+2), Day5 = 20 cm (+1). The smallest increase is +1 between Days 4 and 5. Other intervals show greater growth.
17. The table shows the results of a survey of 200 adults about their favorite season, broken down by age group. Based on the table shown, if one respondent is chosen at random from those who chose Summer, what is the probability that the person is under 40?
    Answer: $\frac{7}{12}$ Summer total = 60. Under 40 includes ages 18-24 (15) and 25-39 (20), totaling 35. Conditional probability = 35/60 = 7/12. Distractor A miscalculates the denominator. Distractor C uses total population instead of Summer subset. Distractor D gives P(Summer) rather than the conditional probability.
18. The table shows the number of books sold by a bookstore in each of four categories during the first and second halves of the year. Based on the table shown, which category had the greatest percent increase from the first half to the second half of the year?
    Answer: Reference Percent increases: Fiction: (480-400)/400 = 20%. Non-Fiction: (360-300)/300 = 20%. Children's: (420-350)/350 = 20%. Reference: (156-120)/120 = 30%. Reference has the greatest percent increase. Distractors A, B, and C all yield 20%, which is a common trap for students who only compute the raw difference (Fiction has the largest absolute increase of 80).
19. The line graph below shows the temperature (°F) recorded every 2 hours from 6 AM to 6 PM on a certain day. Based on the graph shown, during which 2-hour interval was the average rate of temperature change the greatest in magnitude?
    Answer: 4 PM to 6 PM Changes: 6→8 AM: 52-45 = +7. 10→12: 68-60 = +8. 2→4 PM: 76-72 = +4. 4→6 PM: 72-60 = -12. The magnitude |-12| = 12 is the greatest. A student ignoring the negative sign might pick B (+8), and one looking only at the peak area might pick C.
20. Refer to the bar graph below. Approximately what fraction of the total cans recycled over all four weeks was collected in Week 3?
    Answer: about 1⁄4 Heights: Week1 = 150, Week2 = 180, Week3 = 170, Week4 = 200. Total = 700; Week3 is 170⁄700 ≈ 24%, roughly 1⁄4. Other options differ significantly.

Start this quiz