Question

I measured the height of a sample of marigolds by the Union. The values were 7, 10, 12, 9, 10, 12, 10, 9, 10, 11, 8, 12, 10, 9, 11, 10, 9, 10, and 11 inches. I then walked downtown and saw some marigolds growing on Broadway, so I measured a sample of them. The values were 6, 9, 13, 10, 12, 10, 8, 11, 7, 14, 10, 12, 8, 7, 14, 9, 8, 13. Calculate the mean, the variance, and the standard deviation for the Union and Broadway samples. If I wanted to select artificially for different sized marigolds, from which group of plants would I take seeds? Explain.

Answer 1

UNION

The sample size is n=19. The provided sample data along with the data required to compute the sample mean and sample variance are shown in the table below:

	Union	Union2
	7	49
	10	100
	12	144
	9	81
	10	100
	12	144
	10	100
	9	81
	10	100
	11	121
	8	64
	12	144
	10	100
	9	81
	11	121
	10	100
	9	81
	10	100
	11	121
Sum =	190	1932

The sample mean is computed as follows:

Also, the sample variance is

Therefore, the sample standard deviation s is

BROADWAY

The sample size is n=18. The provided sample data along with the data required to compute the sample mean and sample variance are shown in the table below:

	Broadway	Broadway2
	6	36
	9	81
	13	169
	10	100
	12	144
	10	100
	8	64
	11	121
	7	49
	14	196
	10	100
	12	144
	8	64
	7	49
	14	196
	9	81
	8	64
	13	169
Sum =	181	1927

The sample mean is computed as follows:

Also, the sample variance is

Therefore, the sample standard deviation s is

If we wanted to select artificially for different sized marigolds, we should take the seed from the Broadway plants. This is because they have more variability in their heights as compared to union plants, so we will have a mix of different sized marigolds.

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