Question

5 Vera is a shop manager. 5 She has this information about the income in her shop for eight weeks this year. Week 1 2. 3 4 5 6 7 8 Income (thousands of £) 53.5 42.3 39.8 45.1 52.4 19.4 47.9 42.5 The median income for the same eight weeks last year was £49 300 Vera knows that the median income for these eight weeks has decreased this year compared to last year. (a) Work out the percentage decrease of the median income. Give your answer to 2 decimal places. ​

Answer 1

Using the median concept, it is found that it suffered a 11.16% decrease.

What is the median of a data-set?

It is the 50th percentile of the data-set, which is the value that separates the lower 50% from the upper 50%.

In this problem, the ordered data-set, in thousands of £, is given by:

{19.4, 39.8, 42.3, 42.5, 45.1, 47.9, 52.4, 53.5}

It has even cardinality, hence the median is the mean of the 8/2 = 4th and 5th terms, so:

M = (42.5 + 45.1)/2 = £43800.

It decreased from £49300 last year. The percentage decrease is the change divided by initial amount and multiplied by 100%, hence:

P = (49300 - 43800)/49300 x 100% = 11.16%.

More can be learned about the median concept at brainly.com/question/25215461