Question
Use the data set to determine which statements are correct. Check all that apply. 115, 120, 118, 104, 109, 148, 135, 141, 139
a)The median is 120.
b)The median is 109.
c)There is an outlier.
d) The lower quartile is 118.
e)The lower quartile is 112.
f)The upper quartile is 140.
g)The upper quartile is 141.
h))The interquartile range is 28.
Answer:
a)The median is 120.
e)The lower quartile is 112
f)The upper quartile is 140
h)The interquartile range is 28
Step-by-step explanation:
We are given the above Data sets:
115, 120, 118, 104, 109, 148, 135, 141, 139
To confirm the correct options, we have to find the median, lower and upper quartile and the interquartile range
115, 120, 118, 104, 109, 148, 135, 141, 139
We have to find rearrange this numbers from lowest to highest
Hence we have:
104, 109, 115, 118, 120, 135, 139, 141, 148
1) Median
104, 109, 115, 118, 120, 135, 139, 141, 148
The formula for median =
1/2(n + 1)th value
n = number of terms = 9
=1/2(9 + 1)th value
= 1/2(10)th value
= 5th value
The median is the 5th value = 120
Option a) is correct
2) Lower Quartile
The formula for lower quartile=
1/4(n + 1)th value
n = 9
= 1/4(9 + 1)th value
= 1/4(10)th value
= 2.5th value
This means the value is between the 2nd and 3rd values
109= 2nd value
115= 3rd value
First Quartile = 109+ 115/2
= 224/2
= 112
Therefore, Option e)The lower quartile is 112.
3)Upper Quartile
The formula for upper quartile=
3/4(n + 1)th value
n = 9
= 3/4(9 + 1)th value
= 3/4(10)th value
= 7.5th value
This means the value is between the 7th and 8th values
139= 7th value
141 = 8th value
First Quartile = 139 + 141/2
= 280/2
= 140
Therefore, option f)The upper quartile is 140 is correct.
4) The formula for Interquartile range is
Upper quartile - Lower quartile
= 140 - 112
= 28
Therefore, the option h)The interquartile range is 28 is correct.
Looking at the data set below, their is no outlier present.
104, 109, 115, 118, 120, 135, 139, 141, 148
Hence, c)There is an outlier is not correct.
