Question

The Whitcomb Company manufactures a metal ring for industrial engines that usually weighs about 50 ounces. A random sample of 50 of these metal rings produced the following weights (in ounces). 51 53 56 50 44 47 53 53 42 57 46 55 41 44 52 56 50 57 44 46 41 52 69 53 57 51 54 63 42 47 47 52 53 46 36 58 51 38 49 50 62 39 44 55 43 52 43 42 57 49
(a) Construct the frequency table and histogram for these data using eight classes. (You can choose your own classes)
(b) What can you observe about the data from the histogram? tssabout 500 nces. Doyoub elieve their claim? Explain your reason.

Answer 1

Note that the first thing is to always draw up a frequency table to make the plotting process easy, then group your data to a class to make it easier to plot e.g 35-40, 41-45 etc

B)what can be observed is that there is high demand for metal rings that weigh between 50-55 ounces and 55-60 ounces.

Answer 2

Answers:

a) Please refer to the pictures below

b) No.

Step-by-step explanation:

Hi,

A histogram is similar to a bar chart, but the histogram groups numbers into ranges.

The following data can be inferred for the weights:

Range = Highest Value - Lowest Value

= 69 - 36

= 33

Number of classes = 8

$Class\ width = \frac{Range}{Number\ of\ classes}\\= \frac{33}{8}\\= 4.125$

However, once we build the data with this width, some of our values will be left out. So we slightly change the highest and lowest value to help include all our values in this range.

Approximate highest value = 71

Approximate lowest value = 35

New range = 71 - 35

=36

$New\ Class\ width = \frac{36}{8}\\= 4.5$

Using this, we build our frequency table:

The first value is 35, we add 4.5 to it = 39.5

Next we add 4.5 to 39.5 = 44.0

This goes on till we have all our classes:

35.0 - 39.5

39.5 - 44.0

44.0 - 48.5

48.5 - 53.0

53.0 - 57.5

57.5 - 62.0

62.0 - 66.5

66.5 - 71.0

With respect to each of this class width we find the number of values that lie in these intervals, hence the frequency.

The final table looks as shown in the picture below.

To construct a histogram, simply plot the class intervals (on x-axis) against the frequency (on y-axis). The histogram will looks as shown in the picture below.

b)

If you look at the table closely, you will see that the frequency in the more inclined towards the left side. Hence, we say that the distribution is left-skewed.

Furthermore, it can be inferred that the mean and all central values will lie more towards the left side of the graph.

Their claim that their metal rings weighs about 50 ounces can be seen as invalid since all the central values are left-skewed.