Mary records her most recent bowling scores. Her scores are shown below in order from least to greatest.
107,130,136,140,140,142,144,167
Suppose that the score of points changes to points. Answer the following.
(a)What happens to the range?
the range increases by _ points
the range decreases by _ points
The range stays the same.
(b)What happens to the interquartile range (IQR)?
the iqr increases by _ points
the iqr decreases by _ points
The IQR stays the same.
(a) The range is the difference between the highest and lowest scores. In this case, the highest score is 167 and the lowest score is 107. So, the range is 167 - 107 = 60 points. If the score of points changes, the range may increase or decrease depending on the new scores. The given information does not provide enough information to determine how the range would change.
(b) The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1) of the data. To find Q1 and Q3, we need to determine the median (Q2) first. The median of this data set is the average of the middle two scores, which are 140 and 142. So, Q2 = (140 + 142)/2 = 141.
To find Q1, we need to find the median of the lower half of the data set, which are the scores 107, 130, 136, and 140. The median of this lower half is the average of the middle two scores, which are 130 and 136. So, Q1 = (130 + 136)/2 = 133.
To find Q3, we need to find the median of the upper half of the data set, which are the scores 142, 144, and 167. The median of this upper half is the average of the middle two scores, which are 142 and 144. So, Q3 = (142 + 144)/2 = 143.
Therefore, the IQR is Q3 - Q1 = 143 - 133 = 10 points. If the score of points changes, the IQR may increase or decrease depending on the new scores. The given information does not provide enough information to determine how the IQR would change.