forty randomly selected students

Question

Forty randomly selected students were asked the number of pairs of sneakers they owned. Let X = the number of pairs of sneakers owned. The results are as follows.

X Frequency

1	2
2	4
3	7
4	13
5	13
6	1

Find the sample mean x. (Round your answer to two decimal places.)

______

Find the sample standard deviation, s. (Round your answer to two decimal places.)

______

Find the first quartile.

______

Find the median.

______

Find the third quartile.

______

What percent of the students owned at least five pairs? (Round your answer to one decimal place.)

 ______%

Find the 40^th percentile.

______

Find the 90^th percentile.

______

Complete the columns of the chart. (Round your answers to three decimal places.)

X Frequency Relative Frequency Cumulative Relative Frequency

1	2
2	4
3	7
4	13
5	13
6	1

Answer 1

All answers can be found by entering data into a list on a TI-84 calculator (under STAT > Edit...) and using the "1-var-stat" function under STAT > CALC for L1 (or whatever list you enter the data). I will explain how the calculator derives each result.

Mean: Total sum of values/total number of values -> In this case simply add (1 * 2) + (2 * 4) + (3 * 7)... and divide by 40. You should compute 3.85.

Standard deviation: The average distance of each value from the mean of 3.85 -> sqrt(sumSeries(value-3.85)^2)/40) -> 1.21

Median (second quartile): Value in the middle of the dataset (50th percentile) -> 4

First quartile: Split set in two at median, find median of the lesser value set (25th percentile) -> 3

Third quartile: Split set in two at median, find median of the greater value set (75th percentile) -> 5

Percent of students with at least 5 pairs: Simply count all X values of 5 or greater (13 + 1) and divide by total -> 14/40 -> 0.35 -> 35%

For 40th and 90th percentile: You will need to estimate. We know that the 40th percentile will fall between the 25th percentile of 3 and 50th percentile (median) of 4. Given that 40 is closer to 50 than 25, we can estimate that the 40th percentile will be a part of the large set of '4' values close to the median, thus -> 4. For 90th percentile, it will fall between 75th percentile and maximum value (99th percentile) (5 and 6). Since there are 13 values of X = 5 and only 1 value of X = 6, it is safe to say that the 90th percentile of the dataset is -> 5.

For relative frequency in chart: Divide frequency by total values x/40 to get a decimal.

For cumulative frequency: Add previous relative frequency until values total 1. E.g. 0.05, 0.15, 0.325, etc.

I hope this helps, and keep in mind, your TI-84 is your best friend going forward in getting quick and accurate results for questions such as these.