Basic Statistics

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Questions 1 - 10
1

Find the mode of the data set.

Explanation

The mode of a data set is the data point(s) that appear the most often.

In the data set for this problem, both 4 and 5 appear twice, and no other number appears more than twice.

So for this data set there are two modes, 4 and 5.

2

varies directly with . If , what is if ?

Explanation

1. Since varies directly with :

with K being some constant.

2. Solve for K using the x and y values given:

3. Use the equation you solved for to find the value of y:

3

varies directly with . If , what is if ?

Explanation

1. Since varies directly with :

with K being some constant.

2. Solve for K using the x and y values given:

3. Use the equation you solved for to find the value of y:

4

What is the mean of

Explanation

Step 1: Find the sum of the numbers in the set...

Step 2: Count how many numbers are in the set..

There are 10 numbers...

Step 3: Divide the total sum by how many numbers...

So,

5

What is the mean of:

Explanation

Step 1: Find the sum of the numbers

Step 2: Count how numbers there are:

There are numbers..

Step 3: Divide Sum by how many numbers

6

Determine the mean:

Explanation

The mean is the average of all numbers in the data set.

Add the numbers, and divide the total sum by four, since there are four numbers.

The answer is:

7

Stem_and_leaf

Above is the stem-and-leaf display for a group of test scores. Order the mean, the median, and the mode of the scores from least to greatest.

Mean, median, mode

Mean, mode, median

Mode, median, mean

Median, mean, mode

Median, mode, mean

Explanation

The scores represented can be found from matching the tens digits in the "stem" to the units digits that form the "leaves" in their row. For example, the "leaves" in the "5" row are "2 2 4 4 7 7 8", so the scores will be 52, 52, 54, 54, 57, 57, and 58.

There are 53 scores represented, so to find the median, look for the middle score, in position

.

As can be seen in this diagram, the score - the median - is 74.

Stem_and_leaf_1

The most frequently occurring "leaf" is the "6" in the "7" row, so the mode is 76.

The mean is the sum of the scores divided by 53. If we add the scores, we get

, the mean is

In ascending order, the values are mean, median, mode.

8

Determine the range of the numbers:

Explanation

The range is the difference between the highest and lowest numbers.

The highest number is 11.

The smallest number is negative three.

Subtract both numbers. Use parentheses to embrace the negative value.

The answer is:

9

Determine the range of the following numbers:

Explanation

The range is defined as the difference of the highest and lowest numbers.

The highest number is 41.

The lowest number is 3.

Subtract both numbers.

The answer is:

10

What is the mean of:

Explanation

Step 1: Take the sum of all numbers in the set...

Step 2: Count how many elements are in the set...

There are numbers

Step 3: To find the mean, divide the sum by the number of elements..

The mean is

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