Statistics: Descriptive Statistics (High School)
Summarizing data with center, spread, and shape
Statistics: Descriptive Statistics (High School)
Summarizing data with center, spread, and shape
Statistics - Grade 9-12
- 1
The following data show the number of text messages sent by 8 students in one day: 12, 25, 18, 30, 25, 40, 10, 20. Find the mean number of text messages.
The mean is the total of all values divided by the number of values.
The mean is 22.5 text messages. Add the values to get 180, then divide by 8 students: 180 ÷ 8 = 22.5. - 2
The following test scores are listed in order: 68, 72, 75, 80, 84, 88, 91. Find the median score and explain what it represents.
The median score is 80. It represents the middle value, with three scores below it and three scores above it. - 3
A small data set is 4, 7, 7, 9, 10, 10, 10, 12. Find the mode and explain how you know.
The mode is the value that occurs most frequently.
The mode is 10 because it appears more often than any other value in the data set. - 4
The daily high temperatures in degrees Fahrenheit for one week were 62, 65, 70, 68, 66, 64, 71. Find the range.
The range is 9 degrees Fahrenheit. The highest temperature is 71 and the lowest temperature is 62, so 71 - 62 = 9. - 5
The dot plot shows the number of books read by students last month. The data values are 0, 1, 1, 2, 2, 2, 3, 4, 4, 6. Find the median and describe the shape of the distribution.
For 10 values, the median is the average of the 5th and 6th values after the data are ordered.
The median is 2 books. The distribution is skewed right because most values are low, but there is a higher value at 6 that stretches the right side. - 6
The following data show the number of minutes 9 students spent studying: 15, 20, 20, 25, 30, 35, 40, 45, 90. Which measure of center, mean or median, better represents the typical study time? Explain.
Look for a value that is much larger or smaller than the rest of the data.
The median better represents the typical study time because 90 is an outlier that pulls the mean upward. The median is less affected by extreme values. - 7
Find the five-number summary for this data set: 3, 5, 7, 8, 10, 12, 13, 15, 18.
The five-number summary is minimum 3, Q1 6, median 10, Q3 14, and maximum 18. Q1 is the median of 3, 5, 7, 8, which is 6, and Q3 is the median of 12, 13, 15, 18, which is 14. - 8
Use the five-number summary from the data set 3, 5, 7, 8, 10, 12, 13, 15, 18 to find the interquartile range.
The interquartile range measures the spread of the middle 50% of the data.
The interquartile range is 8. Since Q1 = 6 and Q3 = 14, the interquartile range is Q3 - Q1 = 14 - 6 = 8. - 9
A box plot has a minimum of 12, Q1 of 18, median of 25, Q3 of 32, and maximum of 45. What is the interquartile range, and what does it tell you?
The interquartile range is 14 because 32 - 18 = 14. This means the middle 50% of the data values are spread across 14 units. - 10
The prices in dollars of 6 used calculators are 18, 20, 22, 24, 26, and 28. Find the population variance.
For population variance, divide the sum of squared deviations by the number of data values.
The population variance is about 11.67 dollars squared. The mean is 23, the squared deviations are 25, 9, 1, 1, 9, and 25, their sum is 70, and 70 ÷ 6 is about 11.67. - 11
Using the same calculator prices 18, 20, 22, 24, 26, and 28, find the population standard deviation and interpret it.
The population standard deviation is about 3.42 dollars because the square root of 11.67 is about 3.42. This means the calculator prices typically vary by about 3.42 dollars from the mean price. - 12
A histogram shows the number of minutes students spent exercising in one day. Most students are in the 20 to 30 minute and 30 to 40 minute intervals, with fewer students in the 0 to 10 and 50 to 60 minute intervals. Describe the overall shape of the distribution.
Compare the left and right sides of the histogram around the tallest bars.
The distribution is roughly symmetric if the bars decrease in a similar way on both sides of the center. The center appears to be around 30 minutes. - 13
A data set has Q1 = 22 and Q3 = 38. Use the 1.5 × IQR rule to find the lower and upper fences for identifying outliers.
First find the IQR, then subtract 1.5 × IQR from Q1 and add 1.5 × IQR to Q3.
The interquartile range is 16 because 38 - 22 = 16. Since 1.5 × 16 = 24, the lower fence is 22 - 24 = -2 and the upper fence is 38 + 24 = 62. - 14
Two classes took the same quiz. Class A has a mean score of 82 and a standard deviation of 4. Class B has a mean score of 82 and a standard deviation of 12. Compare the two classes.
Both classes have the same average score, but Class B has more variability. Class A's scores are more closely clustered around 82, while Class B's scores are more spread out. - 15
A student scored 78 on a test where the class mean was 70 and the standard deviation was 4. Find the student's z-score and interpret it.
Use z = (data value - mean) ÷ standard deviation.
The student's z-score is 2. This means the student's score was 2 standard deviations above the class mean because (78 - 70) ÷ 4 = 2.