Question

2. The following data represents Math SAT scores for a sample of 10 NCC entering students. 610 540 530 480 530 490 580 590 670 440 For this data: a) [1 pt] Find the mean b) [1 pt] Find the median c) [1 pt] Find the mode d) [2 pts] Find the standard deviation e) [1 pt] Find the variance f) [1 pt] Find the Range g) [1 pt] Find the Interquartile Range (IQR) D alo s h) [3 pts] select the appropriate definition from value such that 20% of the data is less than or equal to it value which is the numerical average of the data most frequent value none of the above I- II- III- IV- • [l pt] Median • [1 pt] Mean [1 pt] Mode

Answer 1

x x-x = x-546 (-x)2 530 I -16 256 480 -66 4356 256 1936 530 590 440 670 -16 44 -106 124 64 -6 -56 11236 15376 4096 36 610 540 3136 490 580 34 1156 Σx = 5460 Σ(x-x) = ο Σ (x-3)? = 41840

Mean= sum of observations/no of observations

=5460/10

=546

Median : Observations in the ascending order are : 440,480, 490, 530,530, 540, 580,590, 610, 670 Here, n = 10 is even. Value of (9)“ observation + value of (* + 1)" observation M = th Value of observation + Value of observation Value of 5th observation + Value of 6th observation 530 + 540 = 535 Mode : In the given data, the observation 530 occurs maximum number of times (2) .: Z = 530

Sample Variance s2 - 2 (x-x)? n-1 41840 = 4648.8889 13 (x - x)2 Sample Standard deviation S = n-1 „/41840 41840 = 4648.8889 = 68.1828

Range =Max observation-min observation

= 670-440

= 230

Interquartile range

The interquartile range is the difference between the third and first quartiles.

The third quartile is 590.

The first quartile is 490.

The interquartile range = 590 - 490 = 100.