Question

Healthy cereal? Researchers collected data on calories per serving for 77 brands of breakfast cereal. The histogram displays the data.

Part (a). Describe the overall shape of the distribution of calories.

Part (b). What is the approximate center of this distribution?

Part (c). Explain why you cannot find the exact value for the maximum number of calories per serving for these cereal brands. Between what two values does it lie?

Part (d). About what percent of the cereal brands have 130 or more calories per serving?

Short answer

Part (a)

Slightly skewed to the left

One gap between 60 and 70 calories

Three potential outliers

Part (b)The center should be between 110 and 120 calories.

Part (c)The maximum number of calories in one serving is between 150 and 160.

Part (d) 10.39%

Step-by-step solution

Part (a) Step 1 Given information. 

Researchers collected data on calories per serving for 77 brands of breakfast cereal. Data show in below

Part (a) Step 2 The overall shape of the calorie distribution

Because the highest bar in the histogram is slightly to the right, with a tail of smaller bars to the left, the distribution is slightly skewed to the left.

We can see that the distribution has a 60-70 calorie gap.

Furthermore, there are three potential outliers because the bar bounded by 50 and 60 calories is separated from the other bars by a gap and has frequency 3.

As a result:

Slightly skewed to the left

One gap between 60 and 70 calories

Three potential outliers

Part (b) Step 1. The distribution's approximate center

The center of the distribution is expected to be at the highest bar in the distribution.

The highest bar in the distribution is bounded by 110 and 120 calories, implying that the center should be between 110 and 120 calories.

As a results:

The center should be between 110 and 120 calories.

Part (c) Step 1 The exact maximum number of calories per serving for these cereal brands

The rightmost bar in the histogram represents the maximum number of calories per serving.

We cannot, however, determine the exact value of the maximum number of calories per serving because we have not been given its exact value and only know a range of possible values for the maximum number of calories per serving from the corresponding bar in the histogram.

We can see in the histogram that the rightmost bar takes on calories between 150 and 160 calories, implying that the maximum number of calories per serving is between 150 and 160 calories.

As a results:

We cannot determine the exact value of the maximum number of calories per serving because we have not been given it and only know a range of possible values for the maximum number of calories per serving from the corresponding bar in the histogram.

The maximum number of calories in one serving is between 150 and 160.

Part (d) Step 1 What percentage of cereal brands have 130 calories or more per serving?

Let us first estimate the frequency off corresponding to each bar's interval, which is given by the bar's height.

Interval	Frequency
50<60	3
60<70	0
70<80	2
80<90	1
90<100	7
100<110	17
110<120	20
120<130	10
130<140	2
140<150	3
150<160	3

Next, add the frequency of all intervals containing at least 130 calories.

$2+3+3=8$

As a result, 8 of the 77 breakfast cereal brands have at least 130 calories per serving.

$$\begin{gathered} \frac{8}{77}\approx 0.1039 \\ 0.1039=10.39\% \end{gathered}$$

As a result, approximately 10.39 percent of cereal brands have 130 or more calories per serving.