Ten public school students had the following scores on their standardized reading test (scores are out of 500): 410, 450, 435, 375, 395, 255, 290, 105, 410, 385 (a) Compute the mean, median, and mode of this data. (b) Compute the first and third quartiles for the data. (c) What do you think is the best measure of center: the mean, median, or mode of the data? Justify your answer.

Ten public school students had the following scores on their standardized reading test (scores are out of 500): 410, 450, 435, 375, 395, 255, 290, 105, 410, 385 (a) Compute the mean, median, and mode of this data. (b) Compute the first and third quartiles for the data. (c) What do you think is the best measure of center: the mean, median, or mode of the data? Justify your answer.

Question
Ten public school students had the following scores on their standardized reading test (scores are out of 500):
410, 450, 435, 375, 395, 255, 290, 105, 410, 385
(a) Compute the mean, median, and mode of this data.
(b) Compute the first and third quartiles for the data.
(c) What do you think is the best measure of center: the mean, median, or mode of the data? Justify your answer.

Answers (1)

2020-11-17

Step 1
It is an important part of statistics . It is widely used .
Mean is defined as the average.
Median is defined as the middl
emost value of the observation such that half of the value lies above it and half below it .
Mode is defined as that value which has the maximum frequency .
Step 2
a)
R CODE :
\(x=c(410,\ 450,\ 435,\ 375,\ 395,\ 255,\ 290,\ 105,\ 410,\ 385)\)
mean(x)
median(x)
OUTPUT :
\(\Rightarrow x=c(410,\ 450,\ 435,\ 375,\ 395,\ 255,\ 290,\ 105,\ 410,\ 385)\)
\(\Rightarrow mean(x)\)
\(\left[1\right] 351\)
\(\Rightarrow median(x)\)
\(\left[1\right] 390\)
There is no mode as all the values have same frequency equal to 1
The required mean is 351 and median is 390
b)
R CODE :
\(quantile(x,0.25)\)
\(quantile(x,0.75)\)
OUTPUT :
\(\Rightarrow quantile(x,0.25)\)
\(25\%\)
311.25
\(\Rightarrow quantile(x,0.75)\)
\(75\%\)
410
The first quartile of the data is 311.25
The third quartile of the data is 410
c)
Median is the best measure of central tendency as it tells the location of the central value .

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