Question

your family moved to a tropical climate. for the first year, you recorded the number of rainy days each month. your data contained 14, 10, 13, 8, 14, 12, 11, 13, 11, 11, 11. if the number of rainy days doubles each month, what statement describes how the mean, mode, median and range will change? a) there isnt enough information. b) the mean will double, but the mode, median and range will stay the same. c) the mean, mode, and median will double, but the range will stay the same. d) the mean, median and range will double. miss susies students heights are 36\, 40\, 36\, 37\, 35\, and 42\. find the mean, median, mode, and range in that order.

Explanation:

Step1: Arrange data in ascending order

The data set is \(8, 10, 13, 13, 14, 14, 11, 11, 11, 12\). Arranged in ascending - order: \(8, 10, 11, 11, 11, 12, 13, 13, 14, 14\).

Step2: Calculate the mean

The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 10\) and \(\sum_{i=1}^{10}x_{i}=8 + 10+11+11+11+12+13+13+14+14 = 117\). So, \(\bar{x}=\frac{117}{10}=11.7\).

Step3: Calculate the median

Since \(n = 10\) (an even number), the median is the average of the \(\frac{n}{2}\) - th and \((\frac{n}{2}+1)\) - th ordered values. \(\frac{n}{2}=5\) and \(\frac{n}{2}+1 = 6\). The 5 - th value is \(11\) and the 6 - th value is \(12\). So, the median \(M=\frac{11 + 12}{2}=11.5\).

Step4: Calculate the mode

The mode is the most frequently occurring value. Here, the mode is \(11\) (it appears 3 times).

Step5: Calculate the range

The range \(R=\text{Max}-\text{Min}\). Here, \(\text{Max}=14\) and \(\text{Min}=8\), so \(R = 14 - 8=6\).
If we double each data - point:
New data set in ascending order: \(16, 20, 22, 22, 22, 24, 26, 26, 28, 28\).
New mean \(\bar{y}=\frac{16 + 20+22+22+22+24+26+26+28+28}{10}=\frac{234}{10}=23.4 = 2\times11.7\).
New median \(N=\frac{22 + 24}{2}=23=2\times11.5\).
New mode \(=22 = 2\times11\).
New range \(=28 - 16 = 12=2\times6\).

The mean, median, mode, and range will double.

Answer:

d) The mean, mode, median and range will double.