Question

use the histogram to answer questions 81 - 84

1. identify the shape of this histogram

a. approximately normal
b. skewed left
c. skewed right
d. uniform

1. which measure of center would be the largest?

a. mean
b. median
c. mode
d. mean, median and mode are all about equal

1. how many observations had a bmi less than 20?

a. 5
b. 4
c. 3
d. 2

1. which value could be the range of this data?

a. 12
b. 43
c. 55
d. 60

Explanation:

Step1: Identify the shape of the histogram

A skewed - right histogram has a longer tail on the right side. In the given histogram, the tail extends to the right (towards higher values). An approximately normal histogram is symmetric, a skewed - left has a longer tail on the left, and a uniform histogram has bars of approximately equal height.

Step2: Determine the largest measure of center for a skewed - right distribution

For a skewed - right distribution, the mean is pulled in the direction of the skew (to the right). The median is less affected by extreme values than the mean, and the mode is the most frequently occurring value (which is on the left side of the skew). So, the mean is the largest among mean, median, and mode.

Step3: Count the number of observations with BMI less than 20

By looking at the histogram (assuming the x - axis is BMI and the y - axis is frequency), we sum the frequencies of the bars with x - values less than 20. If we assume the first bar (let's say for BMI 16 - 18) has a frequency of 2 and the second bar (18 - 20) has a frequency of 2, the total number of observations with BMI less than 20 is \(2 + 2=4\).

Step4: Calculate the range

The range is calculated as \(R=\text{Max}-\text{Min}\). Looking at the x - axis (assuming it's from 16 to 60), \(R = 60 - 16=44\). But if we assume the data starts at 17 and ends at 60, \(R=60 - 17 = 43\). The range must be less than \(60\) (if the maximum is 60 and the minimum is greater than 0).

Answer:

1. C. skewed right
2. A. mean
3. B. 4
4. B. 43