Statistics: Descriptive Statistics Worksheet

Question 1

The numbers of books read by 7 students last month were 3, 5, 2, 8, 5, 4, and 1. Find the mean number of books read.

Accepted Answer

The mean is 4 books. Add the values to get 28, then divide by 7 students: 28 ÷ 7 = 4.

Question 2

The test scores for a small group were 84, 91, 78, 84, 95, and 88. Find the median score.

Accepted Answer

The median score is 86. Put the scores in order: 78, 84, 84, 88, 91, 95. Since there are 6 scores, average the two middle values: (84 + 88) ÷ 2 = 86.

Question 3

The daily high temperatures for one week were 72, 75, 70, 72, 68, 75, and 72 degrees Fahrenheit. Find the mode.

Accepted Answer

The mode is 72 degrees Fahrenheit because it appears 3 times, more often than any other temperature.

Question 4

The numbers of points scored by a basketball team in 5 games were 42, 55, 48, 60, and 50. Find the range.

Accepted Answer

The range is 18 points. The greatest value is 60 and the least value is 42, so 60 - 42 = 18.

Question 5

A dot plot shows the number of pets owned by students in a class. The data values are 0, 1, 1, 2, 2, 2, 3, 4, and 4. What is the median number of pets?

Accepted Answer

The median number of pets is 2. The data are already in order, and the middle value of the 9 numbers is the 5th value, which is 2.

Question 6

The table shows the number of minutes 6 students spent practicing piano: Ana 20, Ben 35, Cara 25, Diego 40, Ella 35, and Finn 25. Find the mean practice time.

Accepted Answer

The mean practice time is 30 minutes. The total is 20 + 35 + 25 + 40 + 35 + 25 = 180, and 180 ÷ 6 = 30.

Question 7

The data set is 6, 9, 12, 12, 15, 18, 24. Find the first quartile, third quartile, and interquartile range.

Accepted Answer

The first quartile is 9, the third quartile is 18, and the interquartile range is 9. The median is 12, so the lower half is 6, 9, 12 and the upper half is 15, 18, 24. The interquartile range is 18 - 9 = 9.

Question 8

A runner recorded these mile times in minutes: 8.5, 8.2, 8.8, 8.4, 8.2, and 8.7. Find the mode and explain what it means.

Accepted Answer

The mode is 8.2 minutes. This means 8.2 minutes was the mile time that occurred most often in the data set.

Question 9

The numbers of text messages sent by 8 students in one day were 14, 22, 35, 18, 22, 40, 16, and 25. Find the median.

Accepted Answer

The median is 22. Put the values in order: 14, 16, 18, 22, 22, 25, 35, 40. The two middle values are 22 and 22, so their average is 22.

Question 10

A teacher recorded quiz scores: 10, 9, 8, 10, 7, 9, 10, and 5. Which measure of center, mean or median, is more affected by the score of 5? Explain.

Accepted Answer

The mean is more affected by the score of 5 because the mean uses every value in the calculation. The median depends mostly on the middle values after the data are ordered, so one low score has less effect on it.

Question 11

The stem-and-leaf plot represents ages at a community art class. Stem 1 has leaves 1, 2, 5, 8. Stem 2 has leaves 0, 3, 3, 7. Stem 3 has leaf 1. The key is 1 | 5 = 15. How many people are represented, and what is the range of ages?

Accepted Answer

There are 9 people represented. The youngest age is 11 and the oldest age is 31, so the range is 31 - 11 = 20 years.

Question 12

The number of goals scored in 9 soccer games was 1, 0, 3, 2, 2, 4, 1, 2, and 5. Find the mean, median, and mode.

Accepted Answer

The mean is about 2.22 goals, the median is 2 goals, and the mode is 2 goals. The total is 20, so 20 ÷ 9 is about 2.22. In order, the data are 0, 1, 1, 2, 2, 2, 3, 4, 5, and the middle value and most common value are both 2.

Question 13

Two data sets show the number of minutes students spent reading. Set A: 10, 12, 13, 15, 15. Set B: 3, 10, 13, 20, 34. Both sets have the same median. Which set has the greater range, and what does that tell you?

Accepted Answer

Set B has the greater range. Set A has a range of 15 - 10 = 5, while Set B has a range of 34 - 3 = 31. This tells us Set B is much more spread out.

Question 14

A bar graph shows the number of students who chose each favorite fruit: apples 6, bananas 4, grapes 8, oranges 5, and strawberries 7. What is the total number of students, and which fruit is the mode category?

Accepted Answer

The total number of students is 30. Grapes are the mode category because grapes had the greatest number of students, with 8 votes.

Question 15

The data set 4, 6, 7, 9, 10, 12, 14, 18 represents hours spent on a project by 8 students. Find the five-number summary: minimum, first quartile, median, third quartile, and maximum.

Accepted Answer

The five-number summary is minimum 4, first quartile 6.5, median 9.5, third quartile 13, and maximum 18. The median is (9 + 10) ÷ 2 = 9.5. The first quartile is (6 + 7) ÷ 2 = 6.5, and the third quartile is (12 + 14) ÷ 2 = 13.

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Statistics: Descriptive Statistics

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