Variance [Binomial Distribution]

The Problem

Let X be a random variable following a Binomial distribution. All Binomial distributions have two parameters: number of trials and success probability. For X, n = 39 and p = 0.39. An example of where such a distribution may arise is the following:

You have a bag of candy made by Statistics, Inc. The company makes only two flavors: sour apple and anchovie. In its processing plant, 39% of the candy made is sour apple. Your bag holds 39 pieces. Define the random variable X as the number of sour apple pieces of candy in your bag.

For those who like pictures, here is a graphic of the probability mass function. Note that the distribution is skewed right:

With this information, calculate the variance of the random variable, σ² or V[X].

Your Answer

In the box below, please enter the variance of the random variable described above, then click on the “Check your answer!” button. Please round your answer to the ten-thousandths place.

Your guess:

Another Binomial Distribution

Would you like to continue working on this topic? If so, click here for another Binomial distribution.

Assistance

Show Formula

Show Solution

Show the R Code

Show the Excel Code

Hide the Excel Code

Copy and paste the following code into your Excel spreadsheet window, making sure the value x ends up in A1 after pasting.

How to calculate the expected value in Excel.
x	P[X=x]	xP[X=x]	x-mu	(x-mu)^2P[X=x]
0	=BINOM.DIST(0,39,0.39,FALSE)	=A2*B2	=A2-B42	=D2^2*B2
1	=BINOM.DIST(1,39,0.39,FALSE)	=A3*B3	=A3-B42	=D3^2*B3
2	=BINOM.DIST(2,39,0.39,FALSE)	=A4*B4	=A4-B42	=D4^2*B4
3	=BINOM.DIST(3,39,0.39,FALSE)	=A5*B5	=A5-B42	=D5^2*B5
4	=BINOM.DIST(4,39,0.39,FALSE)	=A6*B6	=A6-B42	=D6^2*B6
5	=BINOM.DIST(5,39,0.39,FALSE)	=A7*B7	=A7-B42	=D7^2*B7
6	=BINOM.DIST(6,39,0.39,FALSE)	=A8*B8	=A8-B42	=D8^2*B8
7	=BINOM.DIST(7,39,0.39,FALSE)	=A9*B9	=A9-B42	=D9^2*B9
8	=BINOM.DIST(8,39,0.39,FALSE)	=A10*B10	=A10-B42	=D10^2*B10
9	=BINOM.DIST(9,39,0.39,FALSE)	=A11*B11	=A11-B42	=D11^2*B11
10	=BINOM.DIST(10,39,0.39,FALSE)	=A12*B12	=A12-B42	=D12^2*B12
11	=BINOM.DIST(11,39,0.39,FALSE)	=A13*B13	=A13-B42	=D13^2*B13
12	=BINOM.DIST(12,39,0.39,FALSE)	=A14*B14	=A14-B42	=D14^2*B14
13	=BINOM.DIST(13,39,0.39,FALSE)	=A15*B15	=A15-B42	=D15^2*B15
14	=BINOM.DIST(14,39,0.39,FALSE)	=A16*B16	=A16-B42	=D16^2*B16
15	=BINOM.DIST(15,39,0.39,FALSE)	=A17*B17	=A17-B42	=D17^2*B17
16	=BINOM.DIST(16,39,0.39,FALSE)	=A18*B18	=A18-B42	=D18^2*B18
17	=BINOM.DIST(17,39,0.39,FALSE)	=A19*B19	=A19-B42	=D19^2*B19
18	=BINOM.DIST(18,39,0.39,FALSE)	=A20*B20	=A20-B42	=D20^2*B20
19	=BINOM.DIST(19,39,0.39,FALSE)	=A21*B21	=A21-B42	=D21^2*B21
20	=BINOM.DIST(20,39,0.39,FALSE)	=A22*B22	=A22-B42	=D22^2*B22
21	=BINOM.DIST(21,39,0.39,FALSE)	=A23*B23	=A23-B42	=D23^2*B23
22	=BINOM.DIST(22,39,0.39,FALSE)	=A24*B24	=A24-B42	=D24^2*B24
23	=BINOM.DIST(23,39,0.39,FALSE)	=A25*B25	=A25-B42	=D25^2*B25
24	=BINOM.DIST(24,39,0.39,FALSE)	=A26*B26	=A26-B42	=D26^2*B26
25	=BINOM.DIST(25,39,0.39,FALSE)	=A27*B27	=A27-B42	=D27^2*B27
26	=BINOM.DIST(26,39,0.39,FALSE)	=A28*B28	=A28-B42	=D28^2*B28
27	=BINOM.DIST(27,39,0.39,FALSE)	=A29*B29	=A29-B42	=D29^2*B29
28	=BINOM.DIST(28,39,0.39,FALSE)	=A30*B30	=A30-B42	=D30^2*B30
29	=BINOM.DIST(29,39,0.39,FALSE)	=A31*B31	=A31-B42	=D31^2*B31
30	=BINOM.DIST(30,39,0.39,FALSE)	=A32*B32	=A32-B42	=D32^2*B32
31	=BINOM.DIST(31,39,0.39,FALSE)	=A33*B33	=A33-B42	=D33^2*B33
32	=BINOM.DIST(32,39,0.39,FALSE)	=A34*B34	=A34-B42	=D34^2*B34
33	=BINOM.DIST(33,39,0.39,FALSE)	=A35*B35	=A35-B42	=D35^2*B35
34	=BINOM.DIST(34,39,0.39,FALSE)	=A36*B36	=A36-B42	=D36^2*B36
35	=BINOM.DIST(35,39,0.39,FALSE)	=A37*B37	=A37-B42	=D37^2*B37
36	=BINOM.DIST(36,39,0.39,FALSE)	=A38*B38	=A38-B42	=D38^2*B38
37	=BINOM.DIST(37,39,0.39,FALSE)	=A39*B39	=A39-B42	=D39^2*B39
38	=BINOM.DIST(38,39,0.39,FALSE)	=A40*B40	=A40-B42	=D40^2*B40
39	=BINOM.DIST(39,39,0.39,FALSE)	=A41*B41	=A41-B42	=D41^2*B41
Mean:	=SUM(C:C)
Variance:	=SUM(E:E)

When copying this table to Excel, you may want to highlight this note. It seems to help ensure that the code starts in cell A1.

V[X]	the variance (equivalent to σ²)
n	the number of trials
p	the success probability for each trial

V[X]	=	n × p × (1 − p)

	=	39 × 0.39 × (1 − 0.39)

	=	39 × 0.39 × (0.61)

	=	9.2781

© Ole J. Forsberg, Ph.D. 2024. All rights reserved.		.

The Variance

The Problem

Your Answer

Another Binomial Distribution

Assistance