Fred was told he was ranked in the 80th percentile for mathematics in an end of year exam. However, his teacher only posted a list of results, without names, as shown below:21, \, 29, \, 31, \, 33, \, 34, \, 42, \,46, \, 47, \, 49, \, 58, \, 61, \, 63, \, 65, \, 72, \, 76, \, 81, \, 84, \, 87, \, 91, \, 95

If there are 20 people in Fred’s class, what was his class ranking?

What result did Fred receive in the test?

Consider the following data set containing 100 scores in a 10 \times 10 grid:

20	31	37	43	47	54	68	78	84	93
23	31	38	43	47	54	68	78	84	93
23	31	40	44	48	57	70	78	87	94
25	31	40	45	48	57	71	79	87	94
26	32	40	45	49	61	73	80	89	94
27	33	41	45	51	63	73	81	90	96
28	35	41	45	51	64	73	81	90	97
28	36	42	46	51	66	75	82	90	98
29	36	42	46	53	67	75	83	92	99
30	37	43	46	53	68	76	84	92	99

Find the 69th percentile.

Find the 28th percentile.

What is the percentile of 68?

What is the percentile of 43?

Find the 3rd quartile.

Find the 2nd decile.

Find the 7th decile.

Charlie is in a table tennis league. He is ranked third out of 30 people. Calculate in what percentile his team lies.

Roald is in a volleyball competition. His team is ranked 46th out of 180 teams. Calculate in what percentile his team lies. Give your answer to the nearest whole number.

Application

Consider the following chart showing the range of heights for boys aged 10 to 18 years:

(Source: State Government of Victoria, Department of Education and Training)

Lachlan is 15 and his height is at the 9th decile. Select the correct range of heights for Lachlan from the following:

182 - 185\text{ cm}

177 - 181 \text{ cm}

167 - 172 \text{ cm}

158 - 161 \text{ cm}

Quentin is aged 14 and is 150 \text{ cm} tall.

What percentage of boys his age are taller than him?

If Quentin's height continues to follow this growth chart, how tall will he be when he is 18?

Consider the following chart showing the range of heights for girls aged 10 to 18 years:

(Credit: State Government of Victoria, Department of Education and Training)

Rosey is aged 14 and is 160 \text{ cm} tall. What percentage of girls her age are shorter than her?

11.025 Quantiles, deciles and percentiles

Outcomes

MS11-7

What is Mathspace

About Mathspace

20	31	37	43	47	54	68	78	84	93
23	31	38	43	47	54	68	78	84	93
23	31	40	44	48	57	70	78	87	94
25	31	40	45	48	57	71	79	87	94
26	32	40	45	49	61	73	80	89	94
27	33	41	45	51	63	73	81	90	96
28	35	41	45	51	64	73	81	90	97
28	36	42	46	51	66	75	82	90	98
29	36	42	46	53	67	75	83	92	99
30	37	43	46	53	68	76	84	92	99

20	31	37	43	47	54	68	78	84	93
23	31	38	43	47	54	68	78	84	93
23	31	40	44	48	57	70	78	87	94
25	31	40	45	48	57	71	79	87	94
26	32	40	45	49	61	73	80	89	94
27	33	41	45	51	63	73	81	90	96
28	35	41	45	51	64	73	81	90	97
28	36	42	46	51	66	75	82	90	98
29	36	42	46	53	67	75	83	92	99
30	37	43	46	53	68	76	84	92	99

20	31	37	43	47	54	68	78	84	93
23	31	38	43	47	54	68	78	84	93
23	31	40	44	48	57	70	78	87	94
25	31	40	45	48	57	71	79	87	94
26	32	40	45	49	61	73	80	89	94
27	33	41	45	51	63	73	81	90	96
28	35	41	45	51	64	73	81	90	97
28	36	42	46	51	66	75	82	90	98
29	36	42	46	53	67	75	83	92	99
30	37	43	46	53	68	76	84	92	99