Question

a random sample of 25 birth weights (in ounces) is taken yielding the following summary statistics: variable n mean median trmean stdev se mean birthwt 25 129.40 129.00 128.35 17.41 3.48 variable minimum maximum q1 q3 birthwt 96.00 187.00 119.50 135.50 what can be said about the number of outliers for this data set? (a) 0 (b) at least 1 (c) no more than 1 (d) at least 2 (e) no more than 2

Explanation:

Step1: Calculate the inter - quartile range (IQR)

The inter - quartile range \(IQR = Q3 - Q1\). Given \(Q1 = 119.50\) and \(Q3=135.50\), so \(IQR=135.50 - 119.50=16\)

Step2: Calculate the lower and upper bounds for non - outliers

The lower bound \(=Q1 - 1.5\times IQR\). Substitute the values: \(119.50-1.5\times16=119.50 - 24 = 95.5\)
The upper bound \(=Q3 + 1.5\times IQR\). Substitute the values: \(135.50+1.5\times16=135.50 + 24=159.5\)

Step3: Check for outliers

The minimum value is \(96.00\). Since \(96.00>95.5\), the minimum is not an outlier.
The maximum value is \(187.00\). Since \(187.00>159.5\), the maximum is an outlier.

Answer:

B. At least 1