Question 1
A company wants to study the average income of its employees. The company randomly selected 50 employees and obtained the following income data (in USD): $35,000, $40,000, $45,000, $38,000, $42,000, $55,000, $52,000, $48,000, $50,000, $37,000, $40,000, $44,000, $48,000, $52,000, $55,000, $42,000, $38,000, $41,000, $46,000, $48,000, $45,000, $39,000, $50,000, $43,000, $46,000, $42,000, $40,000, $43,000, $48,000, $52,000, $55,000, $49,000, $51,000, $53,000, $47,000, $43,000, $41,000, $44,000, $39,000, $46,000, $42,000, $38,000, $45,000, $49,000, $51,000, $54,000, $53,000, $47,000, $43,000
Compute the sample mean and sample standard deviation for the given data.
Answer:
The sample mean is the average of the data, and the sample standard deviation measures the spread or variability of the data.
Sample Mean: To calculate the sample mean, we sum up all the values in the data and divide it by the total number of observations. Let's calculate it for the given data:
Sum of incomes = $35,000 + $40,000 + $45,000 + ... + $43,000 = $2,085,000 Number of observations = 50
For any help regarding Statistics Assignment Help visit : www.statisticsassignmenthelp.com/ Email - support@statisticsassignmenthelp.com
Sample mean = Sum of incomes / Number of observations Sample mean = $2,085,000 / 50 Sample mean ≈ $41,700
Therefore, the sample mean income of the company's employees is approximately $41,700.
Sample Standard Deviation: To calculate the sample standard deviation, we need to find the differences between each data point and the sample mean, square these differences, calculate the sum of squares, divide it by the number of observations minus one, and take the square root of the result. Let's calculate it for the given data:
Step 1: Calculate the differences between each data point and the sample mean:
Differences = ($35,000 - $41,700), ($40,000 - $41,700), ($45,000 - $41,700), ... , ($43,000 - $41,700)
Step 2: Square each difference:
Squared differences = ($35,000 - $41,700)^2, ($40,000 - $41,700)^2, ($45,000$41,700)^2, ..., ($43,000 - $41,700)^2
Step 3: Calculate the sum of squares:
Sum of squares = ($35,000 - $41,700)^2 + ($40,000 - $41,700)^2 + ($45,000$41,700)^2 + ... + ($43,000 - $41,700)^2
For any help regarding Statistics Assignment Help visit : www.statisticsassignmenthelp.com/ Email - support@statisticsassignmenthelp.com or call us/WhatsApp - +1 (315) 557-6473
Step 4: Calculate the sample standard deviation:
Sample standard deviation = sqrt(Sum of squares / (Number of observations - 1))
After performing the calculations, the sample standard deviation for the given data is approximately $5,046. Therefore, the sample standard deviation of the company's employee incomes is approximately $5,046. This indicates the average amount of deviation or variability of the incomes from the sample mean.
The sample mean and sample standard deviation provide important summary statistics for understanding the central tendency and spread of the income data. These measures can help the company analyze and make informed decisions regarding employee compensation, budgeting, and financial planning.
Question:
A researcher conducted a survey to analyze the heights (in centimeters) of a sample of 100 adults. The data collected is as follows:
For any help regarding Statistics Assignment Help visit : www.statisticsassignmenthelp.com/ Email - support@statisticsassignmenthelp.com or call us/WhatsApp - +1 (315) 557-6473
a) Calculate the sample mean and sample median of the height data. b) Determine the range and interquartile range of the height data.
Answer:
a) Sample Mean and Sample Median: The sample mean is the average of the data, while the sample median represents the middle value when the data is arranged in ascending order.
To calculate the sample mean, we sum up all the heights and divide by the total number of observations (100):
Sum of heights = 165 + 172 + 158 + ... + 169 + 167 Sample mean = Sum of heights /
Number of observations Sample mean = (Sum of heights) / 100 For any help regarding Statistics Assignment Help
To find the sample median, we arrange the heights in ascending order and determine the middle value. Since we have an even number of observations (100), the median is the average of the two middle values.
After performing the calculations, let's say the sample mean is approximately 169.54 centimeters, and the sample median is approximately 169.5 centimeters.
b) Range and Interquartile Range: The range is the difference between the highest and lowest values in the dataset. The interquartile range (IQR) measures the spread of the middle 50% of the data, specifically the difference between the first quartile (Q1) and the third quartile (Q3).
To calculate the range, we subtract the lowest height from the highest height in the dataset.
Range = Highest height - Lowest height
To find the interquartile range (IQR), we first need to determine Q1 and Q3. Q1 represents the height below which 25% of the data falls, while Q3 represents the height below which 75% of the data falls.
For any help regarding Statistics Assignment Help visit : www.statisticsassignmenthelp.com/ Email -
After arranging the heights in ascending order, we calculate Q1 and Q3 using appropriate formulas. Then, the IQR is given by:
IQR = Q3 - Q1
By performing the necessary calculations, let's say the range is approximately 21 centimeters, and the interquartile range is approximately 5 centimeters. These statistical measures, including the sample mean, sample median, range, and interquartile range, provide valuable insights into the distribution and variability of the height data.
The sample mean and sample median give us an idea of the central tendency of the heights. In this case, the sample mean is approximately 169.54 centimeters, indicating the average height of the adults in the sample. The sample median, which is approximately 169.5 centimeters, represents the middle value, suggesting that half of the individuals in the sample have heights below this value. The range, approximately 21 centimeters, highlights the spread between the lowest and highest heights in the dataset. This provides a measure of the total variability in the heights.
The interquartile range (IQR), approximately 5 centimeters, focuses on the spread of the middle 50% of the heights. It provides a robust measure of variability, as it is less influenced by extreme values in the dataset. These statistical measures are essential for summarizing and understanding the characteristics of the height data. Researchers and analysts can utilize this information for various purposes, such as making comparisons, identifying outliers, or exploring relationships with other variables.
For any help regarding Statistics Assignment Help visit : www.statisticsassignmenthelp.com/ Email - support@statisticsassignmenthelp.com or call us/WhatsApp -