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if the mean mark is 5.5
(i) find the value of y,
(ii) calculate the median and mode of the distribution.

y = 9.

Median: 5.

Mode: 5.

Step-by-step explanation:

Express the mean of this distribution about .

Multiple each mark by its frequency. Find the sum of these products. Divide by the sum of frequency.

Sum of products:

.

Sum of frequencies:

.

Mean:

.

.

.

Rank the marks in an increasing order:

.

There are 42 terms. 42 / 2 = 21. What's the 21st mark? . The 21st mark is a 5. That's going to be the median.

Median: 5.

The mode is the item with the greatest frequency.

Mode: 5, with a frequency of 9.

-3.396 = -3.4

-0.708 = -0.7

0.304 = 0.3

0.955 = 1