Question

A council reviews the number of bedrooms in 40 houses located in the same area. The table shows the information gathered. Find the modal average number of bedrooms. Work out the mean number of bedrooms

Answer 1

Mode is the most frequent number, in this case, 3 bedrooms appears 15 times. As a result 3 is the mode.
Doing the mean, is the same as providing a weighted average of bedrooms, with the weights being the frequency a given number of bedrooms appears at. As such, I need to multiply each element of the first column with the respective element of the second column. For example, for 1 bedroom, I have 1 x5 = 5; for 2 bedrooms I have 2x10 =20; if we do this across all number of bedrooms, and then add it all up, we get 113. We then divide this 113, by the number of flats being surveyed ie 40. This gives an average (or mean) of 2.825

Answer 2

The modal average number of bedrooms is 3, while the mean number of bedrooms is 2.825.

What is Mean?

A mean is an arithmetic average of a set of observations. it is given by the formula,

Mean = (Sum of observations)/Number of observations

A.) The modal average number is a mode of a given data set. Now, if the mode of the given data is needed to be taken then we need to observe the row that has the highest frequency.

Therefore, the modal average number of bedrooms is 3.

B.) The mean number of bedrooms can be found as shown below.

Mean number of bedrooms = (1×5 + 2×10 + 3×15 + 4×7 + 5×3)/40

                                               = (5 + 20 + 45 + 28 + 15)/40

                                               = 113/40

                                               = 2.825

Hence, the modal average number of bedrooms is 3, while the mean number of bedrooms is 2.825.

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