AP Statistics : How to interpret histograms

Study concepts, example questions & explanations for AP Statistics

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Example Questions

Example Question #1 : How To Interpret Histograms

Histogram4

 

Based on the histogram, which of the following sets of values was most common in the sample?

Possible Answers:

66-72

64-70

62-68

58-64

54-60

Correct answer:

62-68

Explanation:

You can see from the histogram that the two most frequent ranges for values are 62-64 and 64-66, with 5 values in each group. And from the answer choices, you should see that only one choice, 62-68, contains both of the high-frequency bars.  It also contains the next-highest bar (66-68, with a total of 4), so at 14 total values the range 62-68 has the highest frequency of any of these six-inch-range sets in the choices.

Example Question #1 : How To Interpret Histograms

What is the best measurement of center and spread for the following data set represented by a histogram?

 

Image8

Possible Answers:

Median and Interquartile Range

Mean and Interquartile Range

Mean and Standard Deviation

Median and Standard Deviation

Mean and Range

Correct answer:

Median and Interquartile Range

Explanation:

For skewed distributions, the outliers can greatly affect the value of the mean and the standard deviation. Therefore, the median and IQR would be better measures of center and spread because they are not greatly influenced by outlier values.

Example Question #2 : How To Interpret Histograms

Louie collects data on the amount of sleep students in his class get.

Below is a graphical representation of the data

Sleep

Which of the following is/are false about Louie's class' data?

i: the student with 2 hours of sleep is an outlier

ii: without the student with 2 hours of sleep the data is roughly normally distributed

iii: without the student with 2 hours of sleep the data is slightly right skewed

iv: the student with 2 hours of sleep is within 2 standard deviations of the mean

Possible Answers:

i & ii

i, ii & iii

ii, iii & iv

iii & iv

ii & iv

Correct answer:

ii & iv

Explanation:

Entering the data into a calculator you can quickly find the mean to be 6.5 and the sd to be 1.6 6.5-3.2=3.3 3.3>2 so iv is false and by virtue of this 2 is an outlier so i is true.

 

Between ii and iii, the data is not bell shaped, and does exhibit a slight right skew without the mentioned pt due to more density on 5 and 6 hours than 8 and 9

Example Question #1 : How To Interpret Histograms

Louie collected the following data on sleeping habits of his classmates:

Sleep

Calculate the median, 1st and 3rd quartile (Q1 and Q3) and mode for the data. There are 19 students in the class.

Possible Answers:

Median:7     Q1:6       Q3:8        Mode:6

Median:7     Q1:6       Q3:9        Mode:8

Median:6     Q1:6       Q3:8        Mode:6

Median:6     Q1:5       Q3:8        Mode:6

Median:6     Q1:5       Q3:9        Mode:8

Correct answer:

Median:6     Q1:6       Q3:8        Mode:6

Explanation:

graphing the data, or counting the quarter and halfway points at 10, 15 and 5, results in Q1 and the median both being 6, while Q3 is 8. 6 is the most common value so it is the mode

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