DuPont Automotive is a major supplier of paint to the...

DuPont Automotive is a major supplier of paint to the automotive industry. A survey of 100 randomly selected autos in the luxury car segment and 100 randomly selected autos in the sports car segment that were recently purchased yielded the following colors. (a) Construct a relative frequency distribution for each car type. (b) Draw a side-by-side relative frequency bar graph. (c) Compare the colors for the two car types. Make a conjecture about the reasons for the differences. (TABLE CAN'T COPY)

DuPont Automotive is a major supplier of paint to the automotive industry. A survey of 100 randomly selected autos in the luxury car segment and 100 randomly selected autos in the sports car segment that were recently purchased yielded the following colors.
(a) Construct a relative frequency distribution for each car type.
(b) Draw a side-by-side relative frequency bar graph.
(c) Compare the colors for the two car types. Make a conjecture about the reasons for the differences.
(TABLE CAN'T COPY)

Key Concepts

Survey Sampling Techniques

Survey sampling techniques pertain to the methods used to select a subset of individuals from a larger population to ensure the sample is representative. This is important when drawing conclusions from data, as a properly randomized sample helps reduce bias and supports reliable comparisons between groups.

Comparative Analysis of Categorical Data

This concept involves comparing the distributions of categorical variables across different groups. By analyzing the relative frequency distributions of, for example, car colors between two segments, one can identify patterns, similarities, or differences, and subsequently form hypotheses about the underlying reasons for these observed patterns.

Bar Graphs

Bar graphs are visual tools used to display categorical data through bars, where the height or length of each bar represents the frequency or relative frequency of a category. Side-by-side bar graphs, in particular, are useful for comparing two or more groups simultaneously, making it easier to visually assess similarities or differences across categories.

Relative Frequency Distribution

A relative frequency distribution shows the proportion of observations that fall within each category, calculated by dividing the frequency of each category by the total number of observations. This is crucial for understanding how the categorical data is spread over different groups and allows for comparisons even when the sample sizes differ.

Transcript

00:01 Hello everyone.

00:01 So in this question, a table is given of color, number of luxury cars, and number of sports car.

00:05 So here, in the first segment of this question, we need to construct a table for relative frequency distribution for each of the car type.

00:13 So from this, the relative frequency formula, that is rf is equal to frequency upon frequency divided by the sum of all frequency.

00:24 Sum of all frequency.

00:28 So first of all, we'll calculate the relative frequency for white car in number of luxury cars.

00:34 So for relative frequency of white car, of white luxury car we will be talking about first of all.

00:43 This will be equal to, so we have number of luxury cars as 25, right? and the sum of all frequency comes out to be 100.

00:49 When we do this, this comes out to be equal to 0 .25.

00:53 So once we know how to do the for one car, we can do for a one car.

00:56 Other cars and the same for number of luxury cars and number of sports card.

01:00 So from this, the table obtained for all the values of different cars would be, this table represents the relative frequency of the luxury cars and the sports car for different colors.

01:11 So this was the part a of the question.

01:13 Now we'll move to the second segment of this question in this b segment.

01:16 It is asked, we need to draw a side -by -side relative frequency for graph.

01:20 Bar -graph we need to draw for the relative frequency of all the cars.

01:23 So when we draw the relative frequency side by side bar graph, so it is going to look like this.

01:30 So this is the graph it looks like.

01:32 So here what happens in green color, it is the relative frequency of luxury car and in purple color, it is the relative frequency of sports car...

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