Question

describing distributions in histograms. read the text about each histogram below. describe the distribution shown by calculating the mean, mode, and range. then, write a sentence to describe the shape of the distribution shown in the histogram. 1. paula has a swim meet coming up. she keeps track of the number of laps she swims in each 30 - minute practice leading up to the meet. 44 45 40 35 48 42 39 44 47 46. mean = __ median = mode = 44 range = 90 shape: 2. bryson is a fan of live music. he wants to know if concerts are popular with his peers, so he asks his classmates how many concerts they have attended. 0 0 7 0 1 4 7 4 1 5 4. mean = median = mode = range = shape: __

Explanation:

Step1: Calculate mean for Paula's data

The data set for Paula is \(44,45,40,35,48,42,39,44,47,46\). The sum is \(44 + 45+40 + 35+48+42+39+44+47+46=430\). There are \(n = 10\) data - points. The mean \(\bar{x}=\frac{430}{10}=43\).

Step2: Calculate median for Paula's data

First, order the data set: \(35,39,40,42,44,44,45,46,47,48\). Since \(n = 10\) (an even number of data - points), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered values. \(\frac{44 + 44}{2}=44\).

Step3: Calculate range for Paula's data

The range is the difference between the maximum and minimum values. Range \(=48 - 35=13\).
The shape of Paula's distribution: The histogram shows that the distribution is somewhat symmetric, with most of the data in the \(41 - 45\) and \(46 - 50\) intervals.

Step4: Calculate mean for Bryson's data

The data set for Bryson is \(0,0,7,0,1,4,7,4,1,5,4\). The sum is \(0+0 + 7+0+1+4+7+4+1+5+4 = 33\). There are \(n = 11\) data - points. The mean \(\bar{x}=\frac{33}{11}=3\).

Step5: Calculate median for Bryson's data

Order the data set: \(0,0,0,1,1,4,4,4,5,7,7\). Since \(n = 11\) (an odd number of data - points), the median is the \(\frac{n + 1}{2}=6\)th ordered value, which is \(4\).

Step6: Calculate range for Bryson's data

The range is the difference between the maximum and minimum values. Range \(=7 - 0=7\).
The shape of Bryson's distribution: The histogram shows that the distribution is skewed right, with a large number of values in the \(0 - 1\) interval and a long tail to the right.

Answer:

1. Mean \( = 43\), Median \( = 44\), Range \( = 13\), Shape: Somewhat symmetric
2. Mean \( = 3\), Median \( = 4\), Range \( = 7\), Shape: Skewed right