Question

Height (cm)	Measure 1	168.00	162.80	182.40	155	164.59	182.75	185.50	160.00	185.55	159.2	174	167.64	191.5	175.21	161.50	159.40	175	170.50	146.50	178	173.00	147.50	153	157.48
	Measure 2	168.50	163.00	182.60	156	164.59	183	185.49	161.00	185.62	160	174	170.18	192	175.54	161.50	159.90	174	172.50	146.00	178	174.00	147.40	154.5	158.75
Weight (kg)	Measure 1	116.57	46.27	140.91	59	55.79	80.5	98.42	60.80	124.79	138	136.42	81.65	124.1	74.75	60.01	71.21	84.82	157.50	49.90	69.04	118.95	259.90	178	69.85
	Measure 2	116.12	45.81	139.76	59.4	55.79	80.35	98.52	60.70	124.96	138	136.53	79.38	124.1	74.75	60.50	71.12	85.28	157.00	49.44	69.04	118.95	259.90	178	69.85
Palm Width (cm)	Measure 1	8.00	6.50	10.16	7.10	7.00	8.70	9.53	7.20	8.13	7.4	9.84	6.50	9	8.25	7.62	8.20	8.70	8.26	7.00	8.4	9.35	7.50	7.5	6.80
	Measure 2	8.00	6.80	10.18	7.10	7.10	8.80	9.60	7.10	8.13	7.4	9.84	6.70	9	8.11	7.62	8.10	8.70	8.57	7.00	8.45	9.20	7.40	7.5	7.00
Hand Length (cm)	Measure 1	17.15	18.29	20.32	16.50	16.40	20.10	19.69	17.78	20.07	17.9	17.15	17.10	19.6	18.05	17.78	16.69	18.42	19.05	17.27	19.2	18.10	16.00	16.7	15.90
	Measure 2	17.27	17.78	20.30	16.50	16.30	19.94	19.71	17.78	20.57	17.8	17.15	17	19.6	17.91	17.78	16.69	18.75	18.99	17.53	19.2	18.42	15.90	16.8	15.80
Elbow-grip length (cm)	Measure 1	40.64	33.53	35.56	31.70	34.00	40.00	34.29	34.79	39.37	16.29	40.96	35.56	43.2	32.11	31.75	33.34	38.74	38.10	30.23	35.88	37.78	32.20	33.00	33.00
	Measure 2	40.01	33.53	35.56	32.20	33.60	39.62	34.54	34.29	39.17	16.29	40.64	36.07	43.2	31.89	31.75	33.34	39.01	37.78	30.73	35.88	37.47	32.10	32.40	32.50
Upper arm length (cm)	Measure 1	35.56	35.05	35.05	31.50	34.00	39.80	36.83	32.00	37.59	16.04	36.51	35.56	39.4	37.51	34.29	35.72	38.35	36.35	29.97	38.1	40.64	31.40	35.50	30.00
	Measure 2	36.83	34.29	35.30	31.50	34.50	39.67	36.45	32.26	37.47	15.79	36.83	35.05	39.6	36.23	33.65	35.56	37.85	36.99	29.21	38.1	40.32	31.10	35.30	30.50
Hand Grip Strength 2.0” (kg)	Measure 1	45.00	20.00	48.00	14.00	19.00	52.60	28.58	12.00	49.15	14.5	121	22.00	61	31.12	18.00	33.00	63.00	95.00	18.00	30.00	46.00	29.00	42	37.00
	Measure 2	41.00	18.00	49.00	13.00	23.00	55.50	24.95	13.00	38.55	18	130	21.00	58.5	32.20	17.00	32.00	62.00	97.00	17.00	31.50	48.00	29.00	49	35.00
Hand Grip Strength 2.5” (kg)	Measure 1	45.00	18.00	46.00	12.00	18.00	48.62	21.55	12.00	41.52	13	107	19.00	62	29.18	14.00	34.00	48.00	84.00	12.00	35.00	44.00	26.00	32	25.00
	Measure 2	40.00	18.00	40.00	10.00	22.00	45.25	21.09	11.00	40.55	12	112	18.00	54	27.21	10.00	35.00	46.00	79.00	14.00	32.00	45.50	26.00	34	27.00
Hand Grip Strength 3.0” (kg)	Measure 1	40.00	12.00	38.00	9.00	17.00	42.05	24.27	9.00	45.75	14	100	18.00	52.5	28.54	12.00	31.00	44.00	74.00	16.00	33.50	38.00	22.00	31	27.00
	Measure 2	38.00	12.00	32.00	10.00	18.00	39.10	24.27	8.00	38.1	15.5	94	19.00	48.5	25.50	12.00	30.00	40.00	71.50	11.00	34.00	41.50	23.00	30	24.00
Hand Grip Strength 3.5” (kg)	Measure 1	38.00	12.00	32.00	8.00	14.00	39.05	20.64	10.00	38.5	15	82	12.00	41	24.20	11.00	26.00	40.00	59.00	10.00	32.00	34.00	21.00	29	17.00
	Measure 2	36.00	10.00	28.00	6.00	16.00	37.25	19.73	10.00	36.15	10.5	82	14.00	38.5	23.50	12.00	25.00	42.00	56.00	10.00	30.00	39.00	20.00	28	22.00

note: 24 total participants.

Determine the mean, standard deviation, 5th, and 95th percentile values of all the measurements. (2.5% x 4 value categories)

please show equation even if done on excel

Answer 1

Here, we have to calculate the mean, standard deviation, 5^th and 95^th percentile values of all the measurements.

We have to find these values by using excel.

Excel formula for finding mean is given as below:

=average(range)

Excel formula for finding standard deviation is given as below:

=stdev(range)

Excel formula for finding 5^th percentile is given as below:

=mean + normsinv(0.05)*standard deviation

Suppose you have mean = 5 and sd = 2, then formula becomes,

=5 + normsinv(0.05)*2

Excel formula for finding 95^th percentile is given as below:

=mean + normsinv(0.95)*standard deviation

We know the formula for percentile is given as

X = Mean + Z*SD

Where Z critical value depends on what percentile we have to find.

By using excel, the values for mean, standard deviation, 5^th percentile, and 95^th percentile are summarized in the following table:

Variable	Measure	Mean	Standard deviation	5th Percentile	95th Percentile
Height (cm)	Measure 1	168.168	12.4107	147.7537	188.5813
	Measure 2	168.67	12.3139	148.415	188.9241
Weight (kg)	Measure 1	102.381	50.0206	20.10468	184.6578
	Measure 2	102.219	50.0151	19.95121	184.4863
Palm Width (cm)	Measure 1	8.02667	1.04088	6.314571	9.738762
	Measure 2	8.05833	1.00924	6.398277	9.71839
Hand Length (cm)	Measure 1	17.9671	1.34817	15.74955	20.18462
	Measure 2	17.9779	1.39105	15.68984	20.26599
Elbow-grip length (cm)	Measure 1	34.8342	5.25714	26.18695	43.48139
	Measure 2	34.7321	5.18646	26.20111	43.26306
Upper arm length (cm)	Measure 1	34.6967	4.93519	26.579	42.81433
	Measure 2	34.5979	4.96219	26.43584	42.75999
Hand Grip Strength 2.0” (kg)	Measure 1	39.5396	26.0884	-3.37203	82.4512
	Measure 2	39.7167	27.4624	-5.45503	84.88836
Hand Grip Strength 2.5” (kg)	Measure 1	35.2863	23.5564	-3.46063	74.03313
	Measure 2	34.15	23.3852	-4.31522	72.61522
Hand Grip Strength 3.0” (kg)	Measure 1	32.4421	21.2987	-2.59117	67.47533
	Measure 2	30.7904	19.909	-1.95704	63.53788
Hand Grip Strength 3.5” (kg)	Measure 1	27.7246	17.503	-1.06524	56.51441
	Measure 2	25.9824	19.0022	-5.27339	57.23815