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A number of customers reviewed a music album and rated it out of 5, as shown in the sable below.

a) Work out the range, median and mode of the ratings.
b) The online store wants to use one of these values for the album's average rat
Suggest which value they should use.
Head Over Heels Album: Head Over Heels
The Fractions
Artist: The Fractions
Customer ratings
Rating
5
4
3
2
1
0
Number of customers
10
10
4
8
12
5

1 Answer

4 votes

Final answer:

The range of the album ratings is 5, the median is 2, and the mode is 1. For the album's average rating, the median could be more representative due to the widespread of ratings.

Step-by-step explanation:

To work out the range, median, and mode of the album ratings, we first organize the given data. The number of customers who rated each score (1 to 5) is: 5, 12, 4, 10, 10 respectively.

Range

The range is the difference between the highest and lowest rating. Highest rating is 5 and the lowest is 0, so range = 5 - 0 = 5.

Median

To find the median, arrange all the ratings in ascending order and find the middle number. With 49 total ratings, the median will be the 25th value. Counting up from the lowest rating, we reach the middle in the '2' category, hence the median is 2.

Mode

The mode is the rating given by the most number of customers. As 12 customers rated the album a '1', the mode is 1.

For the album's average rating, the online store could use the mean. However, for discrete data with a notable spread, the median often represents the central tendency better since it is not influenced by extreme values. In this case, the widespread of the ratings and the presence of a mode suggest a non-uniform distribution, where median might be a more representative measure.

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