Question

the histogram shows the starting salaries (rounded to the nearest thousand dollars) for college graduates based on a random sample of recent graduates. determine whether the following statement is true or false according to the graph. the graph is based on a sample of approximately 500 recent college graduates. choose the correct answer below. a. true, because the largest bar has a height of approximately 500. b. false, because the total number of data items is larger. c. false, because the total number of data items is smaller. d. true, because the total number of data items is approximately 500.

Explanation:

Step1: Calculate the total number of data items

Add up the heights of all the bars in the histogram.

$$\begin{align*} &\text{Height of 41 - 45 bar}\approx70\\ &\text{Height of 46 - 50 bar}\approx120\\ &\text{Height of 51 - 55 bar}\approx300\\ &\text{Height of 56 - 60 bar}\approx250\\ &\text{Height of 61 - 65 bar}\approx90\\ &\text{Height of 66 - 70 bar}\approx30\\ \end{align*}$$

$$\begin{align*} \text{Total}&=70 + 120+300+250+90+30\\ &=(70 + 120)+(300+250)+(90+30)\\ &=190+550+120\\ &=860 \end{align*}$$

Step2: Compare with 500

Since \(860>500\), the total number of data items (sample size) is larger than 500.

Answer:

C. False, because the total number of data items is smaller