Question
The weights, in pounds, for 15 horses in a stable were reported, and the mean, median, range, and standard deviation for the data were found. The horse with the lowest reported weight was found to actually weigh 10 pounds less than its reported weight. What value remains unchanged if the four values are reported using the corrected weight?
- Mean
- Median
- Range
- Standard deviation
The correct answer is: Median
○ The concept used in the question id of mean, median, and standard deviation.
○ Mean: Mean is the average value of the given data.
○ Median: Median is the middlemost value of the given data set when data is arranged either in ascending or descending order.
○ Range: Range is thedifference between the highest and lowest observations in a given data.
○ Standard Deviation: Standard Deviation is a measure that shows how much variation from the mean exists.
- Step-by-step explanation:
○ Given:
The horse with the lowest reported weight was found to actually weigh 10 pounds less than its reported weight.
○ Step 1:
As there is change in the weight of horse.
∴ mean will change.
As, mean =
So, if weight changes mean will change
Range will change
As, Range = Maximum value – Minimum value
So, if minimum value change Range will change.
Standard deviation change because mean will change.
Range = Maximum value – Minimum value
Median will remain unchanged.
As, median is central of data and it will not affected by change in lowest value.
∴ median will not change.
- Final Answer:
Correct option.
Option B. median.
The standard deviation is the degree of scatter or dispersion of the data points to their mean in descriptive statistics.
It provides information on the distribution of values within the data sample and verifies how widely apart the data points are from the mean.
A square root of the variance of a sample, statistical population, random variable, data collection, or probability distribution represents its standard deviation.
How to Calculate Standard Deviation
1.) Discover the observations' mean and arithmetic mean.
2.) Find the squared deviations from the mean. (The data value - mean) 2
3.) Calculate the squared difference average. (Variance = The total squared differences divided by the total number of observations)
4.) Determine the variance's square root. (Standard deviation = Square root of variance)
Related Questions to study
The graph of the exponential function h in the xy-plane, where y = h(x), has a y-intercept of d, where d is a positive constant. Which of the following could define the function h ?
An exponential function is a mathematical function with the equation f (x) = an x. where x is a variable and an is a function's base constant. The most typical exponential-function base is the transcendental number e, or approximately 2.71828.
¶The formula for exponential functions is f(x) = bx, where b > 0 and b 1. As with any exponential expression, b and x are referred to as the base and exponent, respectively. Bacterial growth is an illustration of an exponential function. Some bacterial species reproduce hourly.
The graph of the exponential function h in the xy-plane, where y = h(x), has a y-intercept of d, where d is a positive constant. Which of the following could define the function h ?
An exponential function is a mathematical function with the equation f (x) = an x. where x is a variable and an is a function's base constant. The most typical exponential-function base is the transcendental number e, or approximately 2.71828.
¶The formula for exponential functions is f(x) = bx, where b > 0 and b 1. As with any exponential expression, b and x are referred to as the base and exponent, respectively. Bacterial growth is an illustration of an exponential function. Some bacterial species reproduce hourly.
A speed of 60 meters per second is equivalent to z meters per minute. What is the value of z ?
A speed of 60 meters per second is equivalent to z meters per minute. What is the value of z ?
The graph of the linear function f is shown. Which equation defines f ?
The graph of the linear function f is shown. Which equation defines f ?
In the xy-plane, what is the y-intercept of the line with equation y = -2x + 4?
In the xy-plane, what is the y-intercept of the line with equation y = -2x + 4?
(x + 1) = 2 (x + 1)
What value of x satisfies the given equation?
(x + 1) = 2 (x + 1)
What value of x satisfies the given equation?
If 2w + 4t = 14 and 4w + 5t = 25, what is the value of 2w + 3t ?
If 2w + 4t = 14 and 4w + 5t = 25, what is the value of 2w + 3t ?
The total cost to make one batch of soup is . What is the approximate cost per calorie, in cents?
The total cost to make one batch of soup is . What is the approximate cost per calorie, in cents?
The nutrition information for a chicken noodle soup recipe is shown in the table. One batch of soup consists of 6 servings. ( 1 serving cup)
Approximately how many calories from fat are in one serving of the soup?
The nutrition information for a chicken noodle soup recipe is shown in the table. One batch of soup consists of 6 servings. ( 1 serving cup)
Approximately how many calories from fat are in one serving of the soup?
Water quality managers estimate that a population of algae initially covered square miles of water in a nearby river. After a period of time, the algae grew to cover of its original area. Which of the following expressions represents the area of water, in square miles, that the algae covered after this period of time?
Water quality managers estimate that a population of algae initially covered square miles of water in a nearby river. After a period of time, the algae grew to cover of its original area. Which of the following expressions represents the area of water, in square miles, that the algae covered after this period of time?
Which of the following graphs could represent the relationship between the number of manuscripts, , and the cost, , of acquiring ISBNs for the manuscripts?
Which of the following graphs could represent the relationship between the number of manuscripts, , and the cost, , of acquiring ISBNs for the manuscripts?
Costs of some steps to publish a manuscript can vary, as shown in the table.
Ewan writes 30 manuscripts and wants to get them published. What is the minimum cost, in dollars, for professional review of Ewan's manuscripts?
Costs of some steps to publish a manuscript can vary, as shown in the table.
Ewan writes 30 manuscripts and wants to get them published. What is the minimum cost, in dollars, for professional review of Ewan's manuscripts?
What is the solution to the given equation?
What is the solution to the given equation?
The scatterplot shows the average price per square foot of a house in the United States each year for several years. A line of best fit for the data is also shown.
The line of best fit predicted that the average price per square foot in 2001 would be . What is the difference between the predicted value and the actual average price per square foot in 2001 ?
The scatterplot shows the average price per square foot of a house in the United States each year for several years. A line of best fit for the data is also shown.
The line of best fit predicted that the average price per square foot in 2001 would be . What is the difference between the predicted value and the actual average price per square foot in 2001 ?
In the given equation, k is a constant. The equation has no solution. What is the value of k?
An inconsistent system is a set of equations for which no solution exists.
One solution of the system is shown as x = y = z = 0. D must be zero for endless solutions (including non-zero ones). There are thus two possible possibilities for k, but there is only one non-zero answer, e.g.: The value of K can be 2 or 0.5.
In the given equation, k is a constant. The equation has no solution. What is the value of k?
An inconsistent system is a set of equations for which no solution exists.
One solution of the system is shown as x = y = z = 0. D must be zero for endless solutions (including non-zero ones). There are thus two possible possibilities for k, but there is only one non-zero answer, e.g.: The value of K can be 2 or 0.5.
