8.9 Statistics Foundations

Find the mean of: 12, 10, 14, 18, 16. Show the sum and the division.

Find the median of: 22, 19, 15, 18, 21.

Find the mode of: 14, 11, 14, 17, 11, 14, 19.

Find the range of: 8, 13, 6, 17, 11, 20.

A tally chart shows: ★★★★ ★★★ for favourite colour Red (7 students). What is the frequency for Red?

In a class of 30, the frequency table shows: Football 12, Basketball 8, Tennis 5, Other 5. What fraction play Football?

For the data 5, 8, 10, 7, 8, find: (a) mean, (b) median, (c) mode.

A data set has range 12 and minimum value 5. Find the maximum.

For the data 2, 4, 4, 5, 7, 30, identify a potential outlier and justify.

A frequency table: x-value 1, 2, 3, 4; frequency 4, 3, 2, 1. Find the total count.

Find the median of: 20, 17, 14, 11, 19, 16.

The mean of 8, 11, 9, 14 and $x$ is 11. Find $x$.

For the data set 4, 7, 9, 12, 18, find the mean and median.

Find the mean of the frequency table: value 1, 2, 3, 4; freq 5, 3, 2, 2.

A data set has mean 20. If a new value of 50 is added, what is the new mean? (The set had 9 values originally.)

Find the mean, median and mode of: 7, 8, 5, 7, 9, 7, 11, 4.

A class's test marks are 6, 8, 7, 9, 5, 10, 7, 8, 6, 4. (a) Find the mean. (b) Find the median.

A class records the number of pets per student: 0, 0, 0, 1, 1, 1, 1, 2, 2, 3. Construct a frequency table and find the mode.

The range of a set of 6 numbers is 20 and the smallest is 5. The largest is then replaced by 40. Find the new range.

Identify whether each measure (mean, median, mode) is affected by an outlier of 100 added to the data {5, 8, 10, 12}.

A class of 20 students has reaction-distance data (cm): 15, 11, 19, 14, 12, 17, 21, 14, 17, 11, 23, 15, 20, 17, 13, 10, 20, 16, 12, 28. Find the (a) mean, (b) median, (c) range.

For the reaction-distance dataset, identify the value most likely to be an outlier and justify.

Find the missing frequency: $1 \to 3$, $2 \to 5$, $3 \to x$, $4 \to 4$, $5 \to 2$. Total = 20.

The mean of 5 numbers is 12. The mean of 4 of them is 10. Find the 5th number.

A class of 24 has mean test score 62. Adding a 25th student raises the mean to 63. Find the new student's score.

The mean of 8 numbers is 15. One number, 9, is replaced by 25. Find the new mean.

For a frequency table: x = 0, 1, 2, 3, 4; f = 2, 5, 8, 3, 2. Find the median.

A test taker scores $a, b, c, d, e$ where the mean is 75 and median is 78. Two extra results are added: 60 and 90. Find the new mean.

Compare the means of two classes: Class A has 25 students with mean 72; Class B has 15 students with mean 80. Find the combined mean.

A teacher records weekly mark improvements (in %): 3, 5, $-2$, 4, 6, $-1$, 0, 8. Find the (a) mean, (b) range, (c) the number of weeks where improvement was negative.

A data set has mean 16.25 and median 15.5. After removing the largest value (28), find the new mean and median.

Class A: 25 students, mean 70, median 72. Class B: 15 students, mean 80. Find combined mean and discuss whether you can deduce the combined median.

In a set of 6 numbers, the mean is 12, the median is 11.5, the mode is 9, and the range is 14. The numbers are integers and 9 appears twice. Find a possible data set.

A frequency table for grouped data has midpoints 9.5, 13.5, 17.5, 21.5 with frequencies 3, 7, 6, 4. Find the estimated mean.

A set of 7 positive integers has mode 4, median 5, mean 6, and range 9. Find a possible set.

A test produces marks with mean 60, median 62 and mode 70 (a positively skewed distribution). For each of the following changes, state whether mean / median / mode increase, decrease or stay the same: (a) add 100 to every score; (b) remove the score 70 (the only one); (c) multiply every score by 2.

Five numbers have mean 12 and range 6. The smallest is 9. What is the largest? Construct one valid set.

A frequency table has values $x = 1, 2, 3, 4, 5$ with frequencies $f = 2, 5, a, 3, 2$ where the mean is exactly 3. Find $a$.

The mean of the integers 1 to $n$ is 8. Find $n$.

For a list of 6 numbers, mean = median = mode = 7. Construct one valid set, and show it has range 0 or 2.