Question

Listed below are the annual tuition amounts of the 10 most expensive colleges in a country for a recent year. What does this "Top 10" list tell us about the population of all of that country's college tuitions? $52,592 $50,839 $52,109 $53,524 $52,592 2 $52,351 $53,173 $54,148 $52,680 $52,584 Find the mean, midrange, median, and mode of the data set. The mean of the data set is - (Round to two decimal places as needed.) The midrange of the data set is $ (Round to two decimal places as needed.) The median of the data set is (Round to two decimal places as needed.) What is (are) the mode(s) of the data set? Select the correct choice below and, if necessary, fill in the answer box within your choice.

Answer 1

Solution : Let us first arrange the given data points in increasing order to ease the searching of median, 1st quartile and 3rd quartile. The data arranged in increasing order is - 50,839$, 52, 109 $ , 52,351$ 52584$ , 52592$, 52599$ 526808, 531738, 53524$ , 54 148. $

(a) mean of data set - mean - sum of data ne of data points 50839 + 52109 +59351 + 59584 + 52592 + 52592 + 52680 + 53173 +53524 t 54148 526592 =52659.20$

(b) midrange of data set - - mid range = 3rd quartile - C 1st quartile. - 3rd quartile = 75th percentile - = 75% of to data points = Ts x 10 = 7.5th = 8th data point = 53173 $ 10.0

Toc 1st quartile = 25 th peruntile = 25% of to data values - 25 x 10 ~ 25th = 3rd data value F = 59351 $ Note : 3 sid and 8th data values are taken from increasing ordered dater.

I - Midrange = 8th data - 3rd data - = 53173 - 52351 = 822$ 20 = 829.00 $ (c) Median - 50th percentile I n = 10 is even » Median a nth + ( + 1)th = g

10 th + ( 10 ) th 5th data & 6th data 52592 +59592 - 52599 $ = 58592.00 $ (d) Mode & Made is known. as the data point repeating maximum number of times In our case only 52592 is repeating & times and all other data points are 1 time, so Mode = 59599.00 $