Question

Both data sets have a mean of 245. One has a standard deviation of​ 16, and the other has a standard deviation of 24. LOADING... Click the icon to view data sets. Which data set has which​ deviation?

Bold left parenthesis a right parenthesis(a)	2020	88	99			​Key: 2020 ​| 88equals=208208		Bold left parenthesis b right parenthesis(b)	2020
	2121	44	55	88					2121	55
	2222	11	55						2222	22	33	55
	2323	00	00	66	77				2323	00	22	55	88	88
	2424	44	55	66					2424	11	11	22	33	33	33
	2525	11	33	66	88				2525	11	55	88	88
	2626	00	55	99					2626	22	33	44	55
	2727	66							2727	00	55
	2828	33	55	77					2828

A. ​(a) has a standard deviation of 24 and​ (b) has a standard deviation of​ 16, because the data in​ (a) have more variability.

B. ​(a) has a standard deviation of 16 and​ (b) has a standard deviation of ​ 24, because the data in​ (b) have less variability.

Answer 1

We are given the box plots for data set a and b

Box plot for a

Box plot for b

We are given the key 20|8 equals 208

So that we can read the numbers in data set a and b are as follow ,

( The last 3 entries of set a are 283,285 , 287 and of set b are 265,270,275 are not in the above table)

We are given that mean of both the data sets are 245 .

Standard deviation is the measure of the variation or dispersion in the data set.

As the numbers in the data set are more dispersed from the mean or they are away from the mean , then the standard deviation of the data set would be large

If the numbers in the data set are less dispersed from the mean or they are close to the mean , then the standard deviation of the data set would be small.

Comparing the box plot of the both data sets the numbers in the data set "a" are more dispersed from the mean value 245 ( at the middle ) and numbers in the data set "b" are closed or centred towards mean value 245 ( at the middle )

Therefore we can say that data set "a" has large standard deviation than data set "b"

So option A seems to be correct that (a) has a standard deviation of 24 and​ (b) has a standard deviation of​ 16, because the data in​ (a) have more variability.